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Problem 1:

Analyze the data using the methods of this chapter (ANOVA).

· Based on the results, does it appear that there is sufficient evidence to support the claim that the drug lowers pulse rate?

· Are there any serious problems with the design of the experiment?

· Given that only males were involved in the experiment do the results also apply to females?

· The project manager compared the post treatment pulse rates to the mean pulse rate for adult males. Is there a better way to measure the drug’s effectiveness in lowering pulse rates?

· How would you characterize the overall validity of the experiment?

· Based on the available results, should the drug be approved?

· Write a brief report summarizing your findings.

 Placebo Group 10-mg Treatment Group 20-mg Treatment Group 77 67 72 61 48 94 66 79 57 63 67 63 81 57 69 75 71 59 66 66 64 79 85 82 66 75 34 75 77 76 48 57 59 70 45 53

Solution: (a) We need to test the following hypotheses:

\begin{align} & {{H}_{0}}:{{\mu }_{P}}={{\mu }_{10Mg}}={{\mu }_{20\,Mg}} \\ & {{H}_{A}}:\text{Not all the means are equal} \\ \end{align}

We perform an ANOVA analysis with the aid of SPSS. The results are shown below:

The ANOVA table shows that the F-statistics is F = 0.287, and the p-value is p = 0.752, which is greater than the significance level 0.05, which means that we fail to reject the null hypothesis of equal variances. This means that we don’t have enough evidence to claim that the means are not the same, at the 0.05 significance level.

(b) The design doesn't seem to have any serious problem, other than it was applied only to men. If the test was meant to be valid for both men and women, then the design is flawed.

In terms of the assumption for ANOVA, the homogeneity of variance is satisfied as shown in the following table:

The p-value of the test is p = 0.457, which means that we fail to reject the null hypothesis of equal variances.

(c) The results don’t apply to women, since only men participated in the experiment.

(d) For this type of experiment, it would have been convenient to add a four group with subject with normal pulse rates. Then, applying ANOVA we can determine if there is a significant difference between the groups. If there’s a significant difference, we can apply a Post Hoc test to determine with group has a different mean.

(e) If the goal of the experiment is to study the effect of the treatments on the pulse rate of men, the validity doesn’t seem to be seriously flawed. Nevertheless, if the purpose of the test is to assess the effect of the treatments on the pulse rate in general, the validity may be low.

(f) The drug shouldn’t be approved because it doesn’t seem to have a significant effect on the pulse. Besides, since the experiment had only male participants, the conclusions are biased towards one gender.

Problem 2: The VP of HR at the large software company in your region is concerned that the company is not doing enough to recognize generational differences with their employees. She is concerned that younger generations of employees are less satisfied than older generations and, what’s more, that the age-old strategy of paying employees more to increase their satisfaction isn’t working as well with the younger group.

You have been hired by the VP to dig deeper into these issues of generational differences, job satisfaction, and the satisfaction involved with higher income. Working with the dataset labeled “P 6_generational-job-sat”, analyze and interpret the main effects and interaction effects of generation (age category or ‘age_bin’, indicating this is a binary variable) and income (income category or ‘inccat’) on job satisfaction (‘jobsat’). (*Note: both independent variables are measured as categorical variables for all analysis purposes).

• Statement of what analysis you will use to analyze these data
• Acknowledgment of key assumptions of the analysis you use
• Statement of null and alternative hypotheses
• All test statistics and p-values relevant to hypotheses
• Conclusion in terms of hypotheses
• Graphical illustration of the interaction effect (whether or not it is significant)
• Complete interpretation of results (referring to all effects tested), put into the original context of the VP’s concern

Solution: For the sake of the analysis, we will use Job Satisfaction as an interval variable in spite of the fact that it is defined as an ordinal variable. With that assumption in mind, a Two-Way ANOVA will be performed with JobSat as the dependent variable and Age_bin and IncCat as the factors.

We are interested in testing

\begin{align}& {{H}_{0}}:\text{Income doesn }\!\!'\!\!\text{ t have an effect on Job Satisfaction} \\ & {{H}_{A}}:\text{Income has an effect on Job Satisfaction} \\ \end{align}

\begin{align}& {{H}_{0}}:\text{Age doesn }\!\!'\!\!\text{ t have an effect on Job Satisfaction} \\ & {{H}_{A}}:\text{Age has an effect on Job Satisfaction} \\ \end{align}

and

\begin{align} & {{H}_{0}}:\text{ The interaction term is not significant} \\ & {{H}_{A}}:\text{ The interaction term is significant} \\ \end{align}

The assumption of homogeneity of variances is not met, p = 0.000.

The following ANOVA results are obtained:

Notice that the interaction term is significant, F = 10.516, p =0.000. Also, the main effects are significant. In fact IncCat is significant (F = 10.657, p = 0.000) and Age_bin is also significant (F = 176.498, p = 0.000).

Graphically: